[math-fun] Apraphulian rope&pulley XOR ?

I spent a few moments with this paper (thanks for posting!) today & noticed that it showed only NOT, OR, AND, RS flipflop and "multiplex" gates. Is there an elegant XOR in this logic system? Also, it would be interesting to work out an _invertible_ rope&pulley logic system, much closer to (perhaps isomorphic to?) the billiard ball model. Pulleys must be very, very old, as ships & ropes are very old. We know that the Greeks&Romans already had "odometers" in which the number of turns of a wheel would "count" a number of balls, or at least wind a certain amount of rope. Given that we now know they had sophisticated gear trains, it is conceivable that they also had sophisticated rope & pulley mechanisms.